From primordial soup to eusociality; stirring the pot with Hamilton’s ‘Occam’ Rule

Most people will agree that oftentimes people will do something to help someone else out to whom they are related. What researchers are really arguing about is Hamilton’s Rule, which attempts to specify the conditions under which reproductive altruism evolves: r x b > c where b is the benefit (in number of offspring equivalents) gained by the recipient of the altruism. c is the cost (in number of offspring equivalents) suffered by the donor while undertaking the altruistic behavior, and r is the genetic relatedness of the altruist to the beneficiary.[1] As it stands, Hamilton’s equation is a relatively simple, elegant means of describing kin selection in such a way that can be testable. What we see from Hamilton’s Rule is that individuals ought to want to help others if the cost to them is less than the benefit the relative gets prorated by the actual relatedness value.

There are two glaring flaws regarding Hamilton’s Rule that essentially have it sitting dead in the water for any practical application of selection theory within evolutionary biology. The math is too simple, too elegant. Hamilton’s Rule groups a lot of different things and compounds them into just a few variables. Even if it may be true under certain circumstances, even if the math works out, it is ultimately it is just too simple of an equation to explain how cooperation evolves in any real meaningful way.

Though the argument over kin selection vs. group selection has been going on for decades, it is only in recent years that a new dimension to the conversation has emerged via a paper published by Nowak et al. in Nature in 2010 called, “The Evolution of Eusociality.”[2] Eusocial animals are those that live in multigenerational family groups in which the vast majority of individuals cooperate to aid relatively few (or even a single) reproductive group members.[3] As a result, the term is usually applied to colonial insect species of course, which is precisely why the world’s most preeminent natural biologist, E.O. Wilson, is bringing it up. In eusocial species, it is common to have morphological and/or reproductive castes. For example, bees have their workers and their queen. In this case, the queen is responsible for reproduction and as a result, has the morphology to accommodate this responsibility just as the workers cannot reproduce and thus do not have the morphological ability to do so. This is simple enough to understand and most people that study insect behavior agree on this point. However, it gets trickier when researchers operationalize the term ‘eusocial’ as a description for less obvious species, such as humans.

What their paper does is provide a new model for understanding the evolution of eusociality. However, none of this is in the main paper which is only several pages long and really only amount to an abstract of the actual paper which is a 41 page supplement for the Nature article that is very dense, but ultimately boils down to a simple summation, that is to say, individuals in groups have higher reproductive success! Higher reproductive success then, selects for cooperation and group behavior. Well of course it does. In fact, this is essentially a tautology and therefore isn’t even useful as a predictive model because it is going to be true in every circumstance.

What is it about this paper that stirred the pot? Within two months of the publish date there were four responses to this paper, three of which agreed, cheering the authors on. Peter Nonacs of UCLA’s Dept. of Ecology and Evolutionary Biology provided the fourth response in which he says that one of the primary examples the authors used is not actually useful for their argument, and in fact supports the opposite conclusions.[4] In the same issue of Nature was some commentary by Samir Okasha[5], with the notable headline, “Altruism researchers must cooperate.”[6]

And cooperate they did. In March of 2011, Nature published 4 new critiques of the Wilson et al. paper from August of the previous year, signed by more than 150 researchers involved in the discourse.[7] In this response, Abbot et al. take Wilson et al. to task for having a poor grasp of existing theory, resulting in an inability to model cooperation while maintaining a willful ignorance in misrepresenting existing data to support their needs, which, draw unsupported and inappropriate conclusions. How often do you have a paper signed by over 100 researchers taking a strong stance in refutation of what, seemingly offers up only an alternative viewpoint by some notable names? What is all the fuss about?

The fuss isn’t over this one paper. The tension on the subject has been building for several years. And most of those arguments are coming from E.O. Wilson, who is one of the all-time preeminent evolutionary biologists, something that doesn’t seem to be up for debate even amongst his fiercest critics, including Richard Dawkins. Time and again, Dr. Wilson has been raising his substantive voice in opposition of kin selection, even going so far as to call it a gimmick.[8] He’s been doing so for about 12 years now through various papers and high profile publications. Sometimes he’s the sole author, sometimes he’s a co-author, and oftentimes he has been a coauthor with David Sloane Wilson, of group selection fame. And so, these papers have all led up to the 2010 paper, coming back yet again with the same argument that kin selection is wrong, that it doesn’t really explain anything. What does explain evolution of altruism is group selection. Group selection and not kin selection.

The difference this time is that in the, “Evolution of Eusociality,” Wilson isn’t the principle author. Martin A. Nowak and Corina E. Tarnita are both credited before Wilson on the paper, and are both heavyweights in the field of evolutionary mathematical modeling. Indeed, while it’s not for me to say whether Tarnita and Nowak lend Wilson an air of credibility or the other way around, it certainly seems that Wilson felt charged up having two mathematicians raising similar questions regarding the models and evidence for kin selection.

In a 2011 interview in the Boston Globe, Wilson is even more upfront about his distaste for kin selection theory, “Nothing we were finding connected to kin selection, I knew something was wrong. There was a smell to it. Kin selection is wrong.”[9]

And even in their paper, there is a lot of quotes in it that are rather atypical as far as science papers go. The paper itself, rather than promoting a new model, was more geared towards going after the existing paradigm of kin selection, of Hamilton’s Rule. Thus you find quotes like, “This paper is directed at empiricists who still try to test classical Hamilton’s Rule, and theoreticians who try to artificially interpret every result as classical Hamilton’s Rule.”[10] “When the data do not fit, elaborations of inclusive fitness can be constructed that make them fit. The results of the elaborations are Ptolemaic theory constructed of epicycles to keep relatedness at the center of the evolution of social systems.”[11]

And it is here, where I think the paper drew so much criticism, for it isn’t often that scientists write a paper that liken their critics to still believing the Earth is the center of the universe. And let us make no mistake, that is in fact what they are saying. That kin selection is in fact as outdated a model as geocentrism.

In response, Stuart West, who was one of the signers of the response[12] to the Nowak et al. paper writes, “Our letter is in the hope that we will keep non-specialists from wasting time on it. I think it’s so wrong that I don’t think it will have any effect on what people in the field are doing.”[13]

Jerry Coyne, a famous evolutionary biologist at Chicago writes, “It’s simply two guys and a woman deeply misunderstanding evolution and trying to parlay this misunderstanding into fame.”[14] And, “Wilson and his colleagues have been making the same arguments for several years and they’ve already been answered. But like creationists, these guys keep on making the same fallacious claims.”[15] If you’re going to call me a geocentric flat-earther, I’m going to call you a creationist.

And of course, we can’t forget about the Dark Lord of the gene himself, Richard Dawkins who says, “Edward Wilson was misunderstanding kin selection as far back as sociobiology.”[16] Dawkins goes further to say, “It’s almost universally regarded as a disgrace that Nature published it…the reason they published it was the eminence of Wilson and Nowak, not the quality of the paper.”[17]If the paper wasn’t authored by Wilson and Nowak, Nature would never have published it in the first place.

In response, Nowak reiterates the stance he takes in the original paper against his critics, bringing back the epicycles and suggesting that the critics don’t even know what they’re arguing against. “They don’t know what they’re arguing against. The critics don’t understand the math, and moreover, they don’t realize the math is the most important part. That’s like alchemy. There is no other theory than math. Mathematics is the only theory.”[18] Which basically means that if you have a theory for how the world works, but you don’t have the math for it, then it isn’t worth anything. If you have the math for it, then maybe you don’t even need to look at the world. Maybe math is enough.

Are all the leading figures of modern evolutionary biology essentially just a bunch of geocentrist, flat-earther, creationists and alchemists? Is there a real issue about how cooperation evolves, or is it merely a semantic argument between famous guys[19] who don’t like each other?

To answer these questions, we first must ask some others. The controversy seems to revolve around whether the math of Hamilton’s Rule works, and whether it describes what we actually see in the field. Now, Nowak is arguing with Stuart West over Price’s equation:

[20]

What is Price’s equation then? Price’s equation is a nice, intuitive way of looking at selection in terms of kin groups from the standpoint of population genetics. You are looking for the increase of a trait. In terms of eusociality, for helping as an example. This change in frequency is going to be the result of two factors: A) Change due to selection across groups and, B) Change due to selection within groups. In this view, you can divide changes occurring to an allele into one of these categories. And these categories fit very neatly into the compartments of Hamilton’s Rule. The r value = relatedness; b= benefit to others; c = cost to yourself. Thus Hamilton’s Rule is as follows:

Cooperate if rb — c > 0

If Hamilton’s Rule is true, the trait is positively selected and should increase in frequency within the population. If it isn’t true, then the trait will be selected against. And what they are basically arguing about is whether Price’s equation is a general rule, or a special case. West and company, those who signed on against the 2010 Nowak et al. paper is on the side that declares Price’s equation to be a general rule. For them, since Hamilton’s Rule is analogous to Price’s equation for population genetics, it doesn’t matter which way you do it because they are two sides of the same coin.

Nowak et al. is then on the side claiming the equation is only useful in special cases. They argue that in instances where you can use Hamilton’s Rule, that is fine. But the problem lies in the misconceptions and assumptions researchers are guilty of in coming to employ Price’s equation in the first place. It assumes many things about the populations and how selection operates and the effect of mutations and general anomalies. So that, when you take all these things into consideration, Price’s equation is ultimately only useful in a special case. Most of the situations you find in nature aren’t going to be special cases, which makes it inappropriate to use.

If West is correct, then we can think of these models as actor based. For example, if you’re an offspring, do you stay home and help your parents raise more siblings? If you’re off somewhere and you have an opportunity to help someone, do you? In this case, we are looking at the equation from the standpoint of the individual actor portraying the behavior. This is a rather intuitive way to think about the world. Think about it. We don’t say, “Does my gene for helping make me want to help my sibling.” And this is how we can go out and test animal behavior, they are the actors and we observe them to see if they are going to behave in accordance to what our models have predicted. If West and Co. are correct, then we do have this very nice, intuitive model with which to test animal behavior.

Edward Wilson himself, is not known to have any particular prowess in applying mathematics to his research. But Nowak came to evolutionary biology as a mathematician. Furthermore, there is a whole host of other, rather notable figures backing up Nowak et al. in their claims that Price’s equation is a special case. Then again, on the other side is West and a phalanx of well-established researchers defending the old model.

What is starting to resonate with people is some of the problems the Nowak et al. paper brought up regarding Hamilton’s Rule. Suppose we have two actors, A and B. A does something helpful for B, at a cost to A. Traditionally, we can use Hamilton’s Rule to calculate if A will be altruistic to B. If rb > c, then yes A will help B. If rb < c then, according to Hamilton’s Rule, A will not help B. Now suppose A and B are brothers. A is going for a nature walk down by the river. That is when A notices B struggling, in immediate danger of drowning. Should A leap into that stream at great personal risk to themselves? Let’s suppose A does in fact help B out of the stream, then B goes on to have children. Then those children would not have been born without the altruistic behavior of A. In this case, West and company are seeming to say that those children are the rb in Hamilton’s Rule. And then the cost is, what would happen if A jumped in and drowned along with B? Neither one would have children, and they would both be dead. That’s a rather simple cost/benefit analysis.

But now let’s suppose the rescued B doesn’t go off to have his own kids, but rather helps other relatives which in turn gives them the opportunity to go out and have kids. You can still tie this back to the inclusive fitness model because those children would not have happened without action on A’s part, but rb in rb > c becomes less clear as you start to get farther away from the actors involved. And it’s this issue in accounting for indirect effects, where the Nowak et al. paper seems to hold the most water.[21]

The authors do bring up another point as well. Going back to the two actors, A and B, but this time we find them embedded within a group of other inter-related individuals. Now suppose the interaction between A and B is of some public good. Something that not only helps A and B but also benefits the rest of the group as well. In this case, one needs to quit thinking about the relatedness of the individual actors, and start incorporating the inter-relatedness of the entire group with which the central actors are embedded in.[22]

To be clear, it is not impossible to be able to figure out the math from these two examples. The problem is, per Nowak et al. that your typical researchers are guilty of oversimplifying their own observations, because Hamilton’s Rule breaks down once you get any sort of situation that objectively falls outside of the neat little boxes Hamilton’s Rule lays out. To a fault, Hamilton’s Rule cannot deal in non-linearity and synergisms. The more we come to understand the complexity of nature, the more difficult it becomes to find any instances of altruistic behavior that can be place in the simple compartments of Hamilton’s Rule. (rb — c > 0)

References

Abbot, Paul et al. 2011. “Inclusive theory and eusociality.” Nature E1-E4.

Coyne, Jerry. 2011. Why Evolution is True. 04 17. Accessed 04 28, 2017. https://whyevolutionistrue.wordpress.com/2011/04/17/the-boston-globe-on-kin-selection/.

Dawkins, Richard. 2011. Why Evolution is True. 03 24. Accessed 04 28, 2017. https://whyevolutionistrue.wordpress.com/2011/03/24/dawkins-on-nowak-et-al-and-kin-selection/.

Neyfakh, Leon. 2011. “Where does good come from?” Boston Globe, 04 17: http://archive.boston.com/news/science/articles/2011/04/17/where_does_good_come_from/. Accessed 04 28, 2017.

Nonacs, Peter. 2010. “Ground truth is the test that counts.” Nature 661.

Nowak, Martin A. 2012. SuperCooperators: Altruism, Evolution, and Why We Need Each to Succeed. New York: Free Press (Simon and Schuster).

Nowak, Martin A., Corina E. Tarnita, and Edward O. Wilson. 2010. “Evolution of Eusociality.” Nature 1057–1062.

Okasha, Samir. 2010. “Altruism researchers must cooperate.” Nature 653–655.

Pennisi, Elizabeth. 2011. “Researchers Challenge E. O. Wilson Over Evolutionary Theory.” Science http://www.sciencemag.org/news/2011/03/researchers-challenge-e-o-wilson-over-evolutionary-theory.

Seeley, Thomas D., and Paul W. Sherman. 2009. Encyclopedia Britannica. 09 01. Accessed 04 21, 2017. https://www.britannica.com/topic/animal-behavior/Function.

The Editors of Encyclopedia Britannica. 2013. Encyclopedia Britannica. 09 02. Accessed 04 21, 2017. http://www.britannica.com/science/eusocial-species.

[1] (Seeley and Sherman 2009)

[2] (Nowak, Tarnita and Wilson, Evolution of Eusociality 2010)

[3] (The Editors of Encyclopedia Britannica 2013)

[4] (Nonacs 2010)

[5] Samir Okasha is a philosopher of science whose book, “Evolution and Levels of Selection” became the hub through which I conducted the research for this paper.

[6] (Okasha 2010)

[7] (Abbot 2011)

[8] (Neyfakh 2011)

[9] (Neyfakh 2011)

[10] (Nowak, Tarnita and Wilson, Evolution of Eusociality 2010)

[11] (Ibid. n.d.)

[12] (Abbot 2011)

[13] (Pennisi 2011)

[14] (Coyne 2011)

[15] (Ibid. n.d.)

[16] (Dawkins 2011)

[17] (Ibid. n.d.)

[18] (Nowak, SuperCooperators: Altruism, Evolution, and Why We Need Each to Succeed 2012)

[19] I believe it is worth noting that aside from Corina E. Tarnita, all the other major players involved are white men.

[20] Image sourced courtesy of the Wikimedia commons, Wikipedia entry for Price’s Equation. https://en.wikipedia.org/wiki/Price_equation

[21] (Nowak, Tarnita and Wilson, Evolution of Eusociality 2010)

[22] (Ibid. n.d.)

)
Matthew Garvin (高价会)

Written by

UX Design | HCI | Anthropology

Welcome to a place where words matter. On Medium, smart voices and original ideas take center stage - with no ads in sight. Watch
Follow all the topics you care about, and we’ll deliver the best stories for you to your homepage and inbox. Explore
Get unlimited access to the best stories on Medium — and support writers while you’re at it. Just $5/month. Upgrade